Molecule & Life Nonlinear Sciences Laboratory, Research Institute for Electronic Science, Hokkaido University, Kita 20 Nishi 10, Kita-ku, Sapporo 001-0020, Japan.
Phys Chem Chem Phys. 2010 Jul 21;12(27):7636-47. doi: 10.1039/b922596j. Epub 2010 Jun 12.
A framework to calculate the rate constants of condensed phase chemical reactions of manybody systems is presented without relying on the concept of transition state. The theory is based on a framework we developed recently adopting a multidimensional underdamped Langevin equation in the region of a rank-one saddle. The theory provides a reaction coordinate expressed as an analytical nonlinear functional of the position coordinates and velocities of the system (solute), the friction constants, and the random force of the environment (solvent). Up to moderately high temperature, the sign of the reaction coordinate can determine the final destination of the reaction in a thermally fluctuating media, irrespective of what values the other (nonreactive) coordinates may take. In this paper, it is shown that the reaction probability is analytically derived as the probability of the reaction coordinate being positive, and that the integration with the Boltzmann distribution of the initial conditions leads to the exact reaction rate constant when the local equilibrium holds and the quantum effect is negligible. Because of analytical nature of the theory taking into account all nonlinear effects and their combination with fluctuation and dissipation, the theory naturally provides us with the firm mathematical foundation of the origin of the reactivity of the reaction in a fluctuating media.
提出了一种不依赖于过渡态概念来计算多体体系凝聚相化学反应速率常数的方法。该理论基于我们最近开发的一种理论框架，采用了在一级鞍点区域的多维欠阻尼朗之万方程。该理论提供了一个反应坐标，它表示为系统（溶质）的位置坐标和速度、摩擦常数以及环境（溶剂）的随机力的解析非线性函数。在中等偏高的温度下，反应坐标的符号可以确定在热涨落介质中反应的最终目的地，而与其他（非反应）坐标可能取什么值无关。本文表明，反应概率可以解析地推导为反应坐标为正的概率，并且当局部平衡成立且量子效应可以忽略时，通过与初始条件的玻尔兹曼分布进行积分，可以得到精确的反应速率常数。由于该理论考虑了所有非线性效应及其与涨落和耗散的组合，因此该理论自然为我们提供了在涨落介质中反应活性起源的坚实数学基础。
